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attractor, chain recurrent set and limit set of flow

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Science China Mathematics 2000年第3期43卷 244-251页

作者：郑作环 Institute of Applied Mathematics Chinese Academy of Sciences Beijing 100080 China

The properties of attractor, chain recurrent set and limit set of the flow on a compact metric space are studied.

关键词： flow attractor chain recurrent set limit set.

Optimal Strategies Trajectory with Multi-Local-Worlds Graph

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Computers, Materials & Continua 2023年第4期75卷 2079-2099页

作者： Xiang Yu Chonghua Wang Xiaojing Zheng Chaoyu Zeng Brij BGupta School of Electronics and Information Engineering Taizhou UniversityTaizhouZhejiang318000China China Industrial Control Systems Cyber Emergency Response Team Beijing100040China School of Economics and Management Weifang University of Science and TechnologyShouguangShandong262700China National Computer System Engineering Research Institute of China Beijing102699China Department of Computer Science and Information Engineering Asia UniversityTaiwanTaichung413China Research and Innovation Department Skyline University CollegeSharjahP.O.Box 1797United Arab Emirates Staffordshire University Stoke-on-TrentST42DEUK

This paper constructs a non-cooperative/cooperative stochasticdifferential game model to prove that the optimal strategies trajectory ofagents in a system with a topological configuration of a Multi-Local-Worldgraph would converge into a certain attractor if the system’s configuration isfixed. Due to the economics and management property, almost all systems aredivided into several independent Local-Worlds, and the interaction betweenagents in the system is more complex. The interaction between agents inthe same Local-World is defined as a stochastic differential cooperativegame;conversely, the interaction between agents in different Local-Worldsis defined as a stochastic differential non-cooperative game. We construct anon-cooperative/cooperative stochastic differential game model to describethe interaction between agents. The solutions of the cooperative and noncooperativegames are obtained by invoking corresponding theories, and thena nonlinear operator is constructed to couple these two solutions together.At last, the optimal strategies trajectory of agents in the system is proven toconverge into a certain attractor, which means that strategies trajectory arecertainty as time tends to infinity or a large positive integer. It is concluded thatthe optimal strategy trajectory with a nonlinear operator of cooperative/noncooperativestochastic differential game between agents can make agentsin a certain Local-World coordinate and make the Local-World paymentmaximize, and can make the all Local-Worlds equilibrated;furthermore, theoptimal strategy of the coupled game can converge into a particular attractorthat decides the optimal property.

关键词： Multi-Local-world graph stochastic differential game optimal strategy attractor

Improving BDD-based attractor detection for synchronous Boolean networks

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Science China(Information Sciences) 2016年第8期59卷 7-22页

作者： Qixia YUAN Hongyang QU Jun PANG Andrzej MIZERA Faculty of Science Technology and Communication University of Luxembourg Department of Automatic Control & Systems Engineering University of Sheffield Interdisciplinary Centre for Security Reliability and Trust University of Luxembourg

Boolean networks are an important formalism for modelling biological systems and have attracted much attention in recent years. An important challenge in Boolean networks is to exhaustively find attractors,which represent steady states of a biological network. In this paper, we propose a new approach to improve the efficiency of BDD-based attractor detection. Our approach includes a monolithic algorithm for small networks,an enumerative strategy to deal with large networks, a method to accelerate attractor detection based on an analysis of the network structure, and two heuristics on ordering BDD variables. We demonstrate the performance of our approach on a number of examples and on a realistic model of apoptosis in hepatocytes. We compare it with one existing technique in the literature.

关键词： Boolean networks systems biology binary decision diagram attractor verification algorithms

Global attractor for Klein-Gordon-Schrodinger lattice system

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Applied Mathematics and Mechanics(English Edition) 2007年第5期28卷 695-706页

作者：尹福其周盛凡殷苌茗肖翠辉 School of Mathematics and Computational Science Xiangtan University Mathematics and Science College Shanghai Normal University College of Computer and Communicational Engineering Changsha University of Science and Technology

We considered the longtime behavior of solutions of a coupled lattice dynamical system of Klein-Gordon-Schroedinger equation （KGS lattice system）. We first proved the existence of a global attractor for the system considered here by introducing an equivalent norm and using ＂End Tails＂ of solutions. Then we estimated the upper bound of the Kolmogorov delta-entropy of the global attractor by applying element decomposition and the covering property of a polyhedron by balls of radii delta in the finite dimensional space. Finally, we presented an approximation to the global attractor by the global attractors of finite-dimensional ordinary differential systems.

关键词： attractor lattice dynamical system the covering property element decomposition approximation

Global periodic attractor of a class of third-order phase-locked loop

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Science China Mathematics 1997年第7期40卷 707-713页

作者：林源渠 Department of Mathematics Peking UniversityBeijing 100871China

The uniform boundedness and existence of a global periodic attractor for a third-order phase-locked loop with general phase detector characteristics and frequency modulation input is proved under some parametric condi... 详细信息

关键词： global periodic attractor uniform boundedness third-order phase-locked loop frequency modulation input.

Homoclinic and Heteroclinic Flows in Global attractor for Davey-stewartson Ⅱ Equation

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Acta Mathematicae Applicatae Sinica 2008年第4期24卷 599-612页

作者： Zheng-de Dai Shao-lin Li School of Mathematics and Statistics Yunnan University Kunming 650091 China Department of Information and Computing Science Guangxi Institute of Technology Liuzhou 545006 China Department of Mathematics Honghe College Mengzi 661100 China

By the variable transformation and generalized Hirota method, exact homoclinic and heteroclinic solutions for Davey-Stewartson II （DSII） equation are obtained. For perturbed DSII equation, the existence of a global attractor is proved. The persistence of homoclinic and heteroclinic flows is investigated, and the special homoclinic and heteroclinic structure in attractors is shown.

关键词： Persistence Homoclinic And Heteroclinic Flows attractor Davey-Stewarson equation

Finite Dimension of Global attractor of Nonlinear Strain Waves in Elastic Waveguides

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 173-176页

作者： Dacai MA and Murong JIANG(Department of Mathematics, Shangrao Teacher’s College, Shangrao 334000,China)(Department of Mathematics, Yunnan University, Kunming 650091, China)E-mail: jemail@*** Department of Mathematics Shangrao Teacher's College Shangrao 334000 China Department of Mathematics Yunnan University Kunming 650091 China

Consider herein are the finite dimension of global attractor of nonlinearstrain waves in elastic waveguides. By constructing two appropriate bounded coerciveguadratic forms and analysis of evolution of volume in E1 sp... 详细信息

关键词： strain wave attractor Hausdorff and fractal dimensions

attractor FOR WEAKLY DAMPED DRIVEN LONG WAVE-SHORT WAVE RESONANCE EQUATION

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Applied Mathematics(A Journal of Chinese Universities) 1998年第4期13卷 377-384页

作者： GAOHONGJUN LINGUOGUANG LaboratoryofComputationalPhysics InstituteofAppliedPhysicsandComputationalMathematicsP-O-8009Beijing100088. DepartmentofMathematics YunnanUniversityKunming650091.

Abstract The existence of solution and universal attractor for weakly damped driven long wave short wave resonance equation are obtained.

关键词： Long wave-short wave resonance equation attractor

Regularity of Global attractor for Atmospheric Circulation Equations with Humidity Effect

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Acta Mathematicae Applicatae Sinica 2019年第4期35卷 820-829页

作者： Jiao-jiao PAN Qian JIANG Ting-wei RUAN Hong LUO School of Mathematical Sciences Sichuan Normal University

In this article, regularity of the global attractor for atmospheric circulation equations with humidity effect is considered. It is proved that atmospheric circulation equations with humidity effect possess a global attractor in H^k(?, R^4) for any k≥0, which attracts any bounded set of H^k(Ω, R^4) in the H^k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor.

关键词： global attractor regularity atmospheric circulation equations humidity effect